# The National Arithmetic on the Inductive System; Combining the Analytic and Synthetic Methods Forming a Complete Course of Higher Arithmetic

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1858 edition. Excerpt: ...5-day?, B and C in G\$ days, and A and C in G days; in what time would each of them perform the work alone, and how long would it take them to do the work together? Ans. A would do the work in 10 days; B, in 12 days; C, in 15 days; A, B, and C together, in 4 days. 339i To divide a number or quantity into parts, which are proportional to given numbers. Ex. 1. Divide \$250 into two parts which shall be one to the other as 2 to 3. Ans. \$ 100 and \$ 150. opEitTioif. Since the parts 2-j-3 = 5 arc to be propor 5: 3:: S-250: \$ 150, the greater part,"). tional to 2 and 3. 5: 2:: \$ 250: S 100, the less part, Ans' 'l080.s"m, - 5; ' it is evident that the sura of the two numbers, 5, will Iiavc the same ratio to the greater of them, 3, as the amount to be divided, 200, has to the greater of the required parts; and that the sum, 5, will have the same ratio to the less number, 2, as the S 250 has to the less of the required parts; we therefore make two statements, and then find the required term of each proportion as in Art. 337. Hence, .-Is tie sum ofllie gicen numbers is to any one of them, so i the whole quantity lo lie diddtd to the part corresponding to the number used as the second term. Note.--Tliis application of proportion a sometimes called Dislributice or Partititt Proportion. Examples. ' 2. A farmer divides between his three sons 246A. 1R. 32p. of land, sharing it between them as the numbers 3, 4, and 5. What were the shares? Am. 61A. 2R. 18p.; 82A. OR. 21p.; 102A. 2R. 30p. 3. Divide 319 into four parts, that shall be to each other as the numbers 4, G, Gf, and 7. Ans. 55Jff; 85/BY; SGJif; 91ft?. V 4. Standard gold for coinage consists of 9 parts of pure gold, and 1 part alloy. Allowing the alloy to be silver and copper in equal...